Begell House Inc.
Journal of Automation and Information Sciences
JAI(S)
1064-2315
32
10
2000
Optimal Control for Matrix Differential Equation by the Bellman Method
1-10
Fedor G.
Garashchenko
Kyiv National Taras Shevchenko University, Kyiv, Ukraine
Vladimir V.
Pichkur
Kyiv National Taras Shevchenko University, Kyiv
The dynamic programming method is used for solution of the problem of optimal control for matrix differential equation. We adduce the statement about differentiation of certain functions of matrix argument, optimality principle and the Bellman differential equation. The problem of optimal control for the matrix differential equation of the Lyapunov type is solved. The obtained theoretical results are used for solving problems of optimization for estimates of practical stability of linear systems.
Non-Stationary Pontryagin Example with Phase Restrictions
11-17
Nikolay N.
Petrov
Udmurt State University, Izhevsk
A classical non-stationary Pontryagin example with many participants and phase restrictions on a state of an evader under equal dynamic and inertial resources of players is considered.
Stabilization of Non-Autonomous Systems with Respect to a Part of Variables by Means of Controlled Lyapunov Functions
18-25
Alexander L.
Zuev
Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine, Donetsk, Ukraine
The problem about stabilization of a non-autonomous system with respect to a part of variables by means of Lyapunov functions having a negatively defined lower boundary of derivatives is investigated. A theorem on stabilization of non-autonomous system in a sense of differential inclusions is proved. The theorem obtained extends Arstrein theorem to the case of partial stabilization. The constructive feedback design is proposed for linear in control non-autonomous systems provided that there exists a controlled Lyapunov function with respect to a part of variables. For the case of autonomous systems the theorem on partial stabilization under weaker conditions on Lyapunov function is proved.
Direct Approach to a Synthesis of Nonlinear Systems of Stabilization: the Method of Direct Inflexible Synthesis for Linear Canonical Systems of Stabilization
26-34
Sergey M.
Onishchenko
Institute of Mathematics of National Academy of Sciences of Ukraine, Kiev
Potential of realization of the sixth algorithm from a group of six algorithms of direct inflexible synthesis for systems of stabilization.
Convergence of a Matrix Gradient Control Algorithm with Feedback Under Constraints
35-45
Yarema I.
Zyelyk
Institute of Space Research of National Academy of Sciences of Ukraine and National Space Agency of Ukraine, Kyiv, Ukraine
A matrix stochastic regularizing controlling algorithm with feedback for solution of an ill-posed extremum problem is proposed. This algorithm is applicable to a linear control object of arbitrary finite dimension in the presence of additive multidimensional uncorrelated noise under non-stochastic constraints on the unknown matrix of the object's parameters and matrix inputs. The classes of controlled objects and non-controlled disturbances for which the algorithm converges in asymptotic to the fixed point of the algorithm-generating mapping with probability unity, are established.
Linear Differential Hold-In Games with Integral Constraints
46-51
Valentin V.
Ostapenko
Research and Training Complex "Institute of Applied System Analysis" of National Academy of Sciences of Ukraine and Ministry of Education of Ukraine, Kyiv, Ukraine
Irina L.
Ryzhkova
Research and Training Complex "Institute of Applied System Analysis" of National Academy of Sciences of Ukraine and Ministry of Education of Ukraine, Kyiv, Ukraine
The problem of holding trajectory in differential games with an arbitrary matrix and integrated constraints of controls of the players is considered. The method based on concepts of H-convexity and matrix convexity which was earlier applied to solution of linear games with geometrical constraints on controls of the players, is proposed. The analog of the theorem about alternative is obtained.
The Multiple-Choice Sequential Decision Rule with Rejection of Unfortunate Hypotheses
52-58
Sergey Ya.
Zhuk
Kyiv Military Institute of Air Forces, Ukraine
Vladimir I.
Kovalev
Kyiv Military Institute of Air Forces, Ukraine
For the sequential criterion of simple complement we find the estimations of the upper and lower thresholds which are computed on basis of the given conditional probabilities of recognition of a priori probabilities of hypotheses. We obtain the sequential decision rule with rejection of unfortunate hypotheses which uses lower bonds values. We find the range of upper thresholds values in which an one-valued decision about the alternative is made. We analyse the synthesized rule on a model example by means of computer statistical modelling.
On a Heuristic Procedure of Selection of a Finite Set Covering
59-66
Klara G.
Sabiryanova
Institue of Mathematics and Mechanics of Ural brunch of Russian Academy of Sciences, Ekaterinburg, Russia
A monotone stepwise procedure for approximate solution of additive task assignement problem with possible coincidence of some of them is suggested. Such a formulation arises, in particular, under investigation of several travelling salesmen problem, for which at the "assigning" level the optimization in the class of coverings may give a better result than in the class of partitions. Numerical results are presented.
One Approach to Automated Proof of Mathematical Assertions
67-74
Anatoliy I.
Degtyarev
Liverpool University, Great Britain
Alexander V.
Lyaletski
Kyiv National Taras Shevchenko University, Ukraine
Marina K.
Morokhovets
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
We describe the method of theorems proofs search in evironment of an all-in-one mathematical text. The approach is based on the sequential logical calculus of the first order. It contains formal analogues of such natural methods of proofs search as expanding of definitions and application of auxiliary statements or lemmas.
Methods of Synthesis of the New Orthonormal Basic Systems of Generalized Slant-Transforms and Their Fast Algorithms for Image Coding
75-86
Lev A.
Hnativ
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
We propose two fast recursive methods for synthesis of two families of basic systems of generalized slant Walsh transforms when the number of slant vectors k > 2. On this basis the fast algorithms having universal adaptive regular structure with adaptation to the basis word length which enables to parallelize image processing and coding are constructed.
On Assessment of the Insurance Fund Value in the Space Projects Insurance
87-91
A multicriteria approach for assessment of the insurance fund amount in insurance of space projects is proposed. The problem formulation is considered, the qualitative analysis is performed and a method of multicriteria solution of the space project insurance problem under uncertainty conditions is suggested. It is proved that the tendency of insurance fund reduction possesses the ergodicity property.